An exact solution of the nonlinear Poisson-Boltzmann equation in parallel-plate geometry

Nonlinear Poisson-Boltzmann solutions for charged parallel plates: When opposite charges repel

I present an exact solution of the Poisson-Boltzmann equation for two parallel plates and discuss the solution properties. I discuss in more detail plates with opposite charges: In this case, there are two critical separations, Lc,1 < Lc,2. For separations less than Lc,1, the force between plates is repulsive. It switches to attractive at Lc,1, but with the electric potential having the same sign on both plates. For L > Lc,2, the force remains attractive, and the potential at the plates has the same sign as the charge on each plate. I also describe charge regulation, determined by pKa, and provide formulas for both the critical distance where oppositely charged plates repel and their charging process. The implications of these results for the nanoparticle assembly, as driven by electrostatic interactions, are also discussed.

Effect of Roughness and Elasticity on Interactions between Charged Colloidal Spheres

The effects of realistic roughness and elasticity on the interactions between charged silica spheres are studied as a function of surface potential, screening length, interfacial energy, and roughness. The repulsive force F_rep that must be overcome to bring charged spheres into contact is relatively insensitive to elasticity unless spheres are hundreds of times softer than silica. F_rep is also insensitive to roughness and interfacial energy. In contrast, roughness has a large effect on the binding energy of spheres and the force F_sep to separate them. Both are lowered by 1 to 2 orders of magnitude by the measured surface roughness of less than 1 nm on 1 μm silica spheres. The reason is that interactions between rigid spheres are dominated by the highest surface peaks rather than the entire spherical surface. Elasticity can increase the pull-off force of rough spheres by a factor of 2 or more because additional surface area can be brought into contact. The implications of these results for shear-thickening transitions are discussed.